Heart-lung machines of this type are known, for example, as portable devices for emergency use. It is a problem in this respect that it must be ensured with devices of this type prior to the putting into operation that there is no longer any air in the blood-conducting components of the extracorporeal blood circuit, since this could seriously endanger a patient. A so-called priming liquid is therefore filled in and the extracorporeal blood circuit is vented or deaerated prior to the putting into operation in order to eliminate the air bubbles present in the blood-conducting components. This is, however, time-consuming with the known apparatus.